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A137336 Triangle read by rows, with 2-variable g.f. (-2*x*t+t^2)/(1-2*x*t+t^2). 0
0, 0, -2, 1, 0, -4, 0, 4, 0, -8, -1, 0, 12, 0, -16, 0, -6, 0, 32, 0, -32, 1, 0, -24, 0, 80, 0, -64, 0, 8, 0, -80, 0, 192, 0, -128, -1, 0, 40, 0, -240, 0, 448, 0, -256, 0, -10, 0, 160, 0, -672, 0, 1024, 0, -512, 1, 0, -60, 0, 560, 0, -1792, 0, 2304, 0, -1024 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row sums are {0, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11}.

REFERENCES

Rosenblum and Rovnyak, Hardy Classes and Operator Theory,Dover, New York,1985, page 18-19

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

Triangle begins:

{0},

{0, -2},

{1, 0, -4},

{0, 4, 0, -8},

{-1, 0, 12, 0, -16},

{0, -6, 0, 32,0, -32},

{1, 0, -24, 0, 80, 0, -64},

{0, 8, 0, -80, 0, 192,0, -128},

{-1, 0, 40, 0, -240, 0, 448, 0, -256},

{0, -10, 0, 160, 0, -672, 0, 1024, 0, -512},

{1, 0, -60, 0, 560, 0, -1792, 0, 2304, 0, -1024}

...

MATHEMATICA

p[t_] = (-2*x*t + t^2)/(1 - 2*x*t + t^2);

Table[ ExpandAll[SeriesCoefficient[Series[p[t], {t, 0, 30}], n]], {n, 0, 10}];

a = Join[{{0}}, Table[ CoefficientList[ExpandAll[SeriesCoefficient[Series[p[t], {t, 0, 30}], n]], x], {n, 0, 10}]]; Flatten[a]

(* polynomial recursion: needs first three terms: *)

p[x, 0] = 0; p[x, 1] = -2*x; p[x, 2] = 1 - 4*x^2; p[x_, n_] := p[x, n] = 2*x*p[x, n - 1] - p[x, n - 2];

Table[ExpandAll[p[x, n]], {n, 0, Length[g] - 1}]

CROSSREFS

Sequence in context: A130125 A317552 A214809 * A115322 A053117 A121448

Adjacent sequences:  A137333 A137334 A137335 * A137337 A137338 A137339

KEYWORD

tabl,sign

AUTHOR

Roger L. Bagula, Apr 07 2008

STATUS

approved

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Last modified March 29 18:26 EDT 2020. Contains 333116 sequences. (Running on oeis4.)